The non-abelian Iwasawa Main Conjecture

Let $K_n$ be a tower of finite Galois extensions of ${\Bbb Q}$ with Galois groups $G_n$, let $G_\infty=\varprojlim G_n$ be a $p$-adic Lie group of dimension at least $1$, and let $\Lambda={\Bbb Z}_p[[G_\infty]]=\varprojlim {\Bbb Z}_p[G_n]$. Let $M$ and $S$ be as in the paper's notation, let $p\neq 2$, let $T_B\subset M_B$ be a lattice with $T_p=T_B\otimes{\Bbb Z}_p$ Galois stable, and let $k$ be big enough. The compatible finite-level generators define $\delta_p(G_\infty,M,k)$.

Non-abelian Main Conjecture. The element $\delta_p(G_\infty,M,k)$ is induced by a generator

$$\widetilde{\delta}_p(G_\infty,M,k)\in \operatorname{det}_{\Lambda}R\Gamma({\Bbb Z}[1/S],\Lambda\otimes T_p(k))\otimes \operatorname{det}_{\Lambda}(\Lambda\otimes T_B(k-1))^+.$$

This is the Iwasawa-theoretic deformation of the equivariant Bloch–Kato conjecture to a possibly non-commutative Iwasawa algebra. The paper states that the finite-level equivariant Bloch–Kato conjecture for all $G_n$ is equivalent to this Main Conjecture.